A Split-step Algorithm for Solving Wave Equations and Its Numerical Simulation |
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Author | WangLei |
Tutor | YangDingHui |
School | Tsinghua University |
Course | Mathematics |
Keywords | split-step algorithm weighted nearly analytic discrete method numerical dispersion computational efficiency 3D seism modeling |
CLC | P631.4 |
Type | Master's thesis |
Year | 2009 |
Downloads | 87 |
Quotes | 0 |
The SSA is a new numerical method for solving wave equations. We first transform the second-order PDE into a system of first-order PDEs and then the high-order spatial derivatives can be approximated by the interpolations of the displacement, particle-velocity, and their gradients. Third-order implicit Adams method and differentiator series method are applied to solve the semi-discrete differential equation, so the explicit SSA is developed. Theoretical and numerical results show that the SSA can effectively suppress numerical dispersion and improve computational accuracy and efficiency.This paper studies the theoretical properties of the SSA, including the stability criteria, theoretical error and numerical error, numerical dispersion and computational efficiency. Numerical simulations for 2D acoustic- and elastic wave fields are presented. Seismic stress-fields simulations using the WNAD method are compared with the results obtained by the NAD method, the LWC and the SG. Meanwhile, a weighted SSA is developed and its stability criteria, numerical dispersion, and computational efficiency are studied. Numerical simulations of the WSSA for 2D complex medium are also presented. We also extent the SSA to 3D case and develop the 3D WSSA.Numerical results show that the computational speed of the SSA is about 40 times of the SG and about 16 times of the LWC and the SSA requires only about 18% of storage space of the SG and about 28% of storage space of the LWC to achieve the same computational accuracy. The computational costs and memory storage requirements of the WNAD method are less than those of the NAD method, the LWC and the SG. The WSSA is more economical than the SSA, and can suppress numerical dispersions more effectively.